Document WO 99/46055 discloses such a device in which a spherical closure element that closes off the outlet of the reservoir is ejected by the blast of air generated by an air blaster. More particularly for using a powder dispenser device, the air pressure necessary to actuate the device must be high enough to guarantee that the dose is dispensed in full, and that it is broken up if necessary. In the above-mentioned device, the air pressure required to actuate the device is determined by the resistance of the ball to being ejected. That resistance is relatively difficult to control and to predetermine since it depends on the friction between the ball and its cylindrical seat in which it is fitted to close off said reservoir in leaktight manner. Therefore, it can be necessary to minimize the interference between the sphere and its cylindrical seat, which naturally can degrade the effectiveness of closure. In addition, it can be necessary to minimize the depth and the positioning of the sphere in its seat in order to facilitate ejecting it. It can also be necessary to provide air pressure that is relatively high and that is not always easy to achieve by means of a pump system or of a bellows system, in particular when such air blasters are actuated manually by the patient. In addition, the dispensing, i.e. the ejection of the ball from its seat, can take place at various lengths of the stroke of the pump or of the bellows of the air blaster, so that the precise instant at which the fluid or powder is dispensed cannot always be predetermined exactly. Finally, the choice of materials for the sphere and for its seat is limited.